SSC Study Materials: Lines and Angles

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SSC Study Materials: Lines and Angles

Fundamental terms and Definitions:

  1. Line segment and ray: The part of a straight line whose both ends are fixed is called a line segment. If one point of a line is fixed, it is called a ray.
  2. Collinear points and Non-collinear points: If three or more points lie on a straight line, they are called collinear points. If three or more points do not lie on a straight line, they are called non-collinear points.
  3. Types of angles: According to measurement, angles are of the following types.
    • Acute angle: If an angle lies between 0° and 90°, it is called an acute angle.
    • Right angle: An angle whose measurement is 90° is called a right angle.
    • Obtuse angle: If an angle lies between 90° and 180°, it is called an obtuse angle.
    • Straight angle: An angle whose measurement is 180° is called a straight angle.
    • Reflex angle: If an angle lies between 180° and 360°, it is called a Reflex angle.
  4. Complementary angles and Supplementary angles: If the sum of two angles is equal to 90°, they mutually formed a set of complementary angles; e.g., the Complementary angle of 30° is 60° and the Complementary angle of 60° is 30°.

If the sum of two angles is 180°, they are called supplementary to each other; e.g. Supplementary angle of 60° is 120° and the supplementary angle of 120° is 60°.

  1. Adjacent angles: Two angles are said to be adjacent angles if they have a common vertex, a common side, and their uncommon sides are situated at two different sides of the common side.

In the adjacent figure, ∠EBC and ∠DBC are adjacent angles because point B is common to both of them and their uncommon sides BD and BE are opposite to the common side BC.

Similarly ∠DBC and ∠DBA are adjacent angles, but ∠EBC and ∠DBA are not adjacent angles as they do not have a common side.

  1. Linear pair of angles: In the adjacent figure ∠AOC and ∠COB are adjacent angles and AOB is a straight line i.e., uncommon sides of adjacent sides form a straight line. Such angles are called linear pairs of angles.
  2. Vertically opposite angles: If two straight lines AB and CD intersect each other at point O, then angles facing each other are called vertically opposite angles.

In the adjacent figure, ∠AOD and ∠BOC are one pair of vertically opposite angles, while ∠AOC and ∠BOD are another pair of vertically opposite angles.

  1. Transversal line: A straight line intersecting two or more lines at different points is called a transversal line.

In the given figure straight line n intersects two different lines l and m respectively at points P and Q, so line n is a transversal line.

  1. Exterior angles and Interior angles: In the figure given below, a transversal line n intersects two straight lines l and m respectively at P and Q. Around each point P and Q, four angles are formed, among these angles ∠1, ∠2, ∠7, ∠8 are called exterior angles while ∠3, ∠4, ∠5, ∠6 are called interior angles.
  2. Corresponding angles and Alternate angles: In the figure drawn above
    • ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, and ∠4 and ∠8 are called pairs of corresponding angles.
    • “∠4 and ∠6” and “∠3 and ∠5” are called pairs of alternate interior angles.
    • ∠1 and ∠7″ and “∠2 and ∠8” are called alternate exterior angles.
    • ∠4 and ∠5″ and “∠3 and ∠6” are called consecutive interior angles Alternate interior/exterior allied angles or co-interior angles.

All type of alternate angles is commonly known as alternate angles.

  1. Exterior angle and Interior opposite angle of a triangle: In the adjacent figure sides BC, CA, and AB of triangle ABC are respectively produced to points D, E, and F. ∠ACD, ∠BAE, and ∠CBF thus formed are called exterior angles of the triangle.

Interior angles ∠A and ∠B are called interior opposite angles to the exterior angle ∠ACD. Similarly, ∠B and ∠C are interior opposite angles to the exterior angle BAE etc.

  1. Types of triangles according to sides:
    • Equilateral triangle: When all the sides of a triangle are equal, it is called an equilateral triangle.
    • Isosceles triangle: If any two sides of a triangle are equal, it is called an isosceles triangle.
    • Scalene triangle: If the sides of a triangle are unequal, it is called a scalene triangle.
  2. Types of triangles according to their angles:
    • Acute angle triangle: If all three angles of a triangle are acute, then the triangle is called an acute angle triangle.
    • Right angle triangle: If one of the angles of a triangle is right angled (= 90°) then it is called a right angle triangle.

A triangle has at most one right angle.

  • Obtuse angle triangle: If one of the angles of a triangle is obtuse (lies between 90° and 180°) then

it is called an obtuse angle triangle.

A triangle has at most one obtuse angle.

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